Face Recognition.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "414c7ae7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cee20731",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4916, 576)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.genfromtxt(\"faces.txt\", delimiter=None)\n",
    "plt.figure()\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60ed46fc",
   "metadata": {},
   "source": [
    "The matrix represents the dataset of human faces, where there are 4916 pictures each with 576 pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f3d47757",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x13a5ad3c0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = np.mean(X, axis=0, keepdims=True)\n",
    "img = np.reshape(mu,(24,24))\n",
    "plt.imshow( img.T , cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18b7455b",
   "metadata": {},
   "source": [
    "Derive and plot the mean face image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0161b49d",
   "metadata": {},
   "outputs": [],
   "source": [
    "X0 = X - mu"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46024482",
   "metadata": {},
   "source": [
    "Gain the mean subtracted matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ed4068b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4916, 576)\n",
      "(576, 576)\n",
      "(576, 576)\n"
     ]
    }
   ],
   "source": [
    "U, S, Vh = np.linalg.svd(X0, full_matrices=False)\n",
    "Sigma = np.diag(S)\n",
    "print(U.shape)\n",
    "print(Sigma.shape)\n",
    "print(Vh.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8dfd3b9",
   "metadata": {},
   "source": [
    "Singular Vector Decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9273dc21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "W = U.dot(Sigma)\n",
    "K = list(range(1, 31))\n",
    "mse = np.zeros((len(K),))\n",
    "for k in K:\n",
    "    Xhat0 = W[:,:k].dot( Vh[0:k,:] )\n",
    "    mse[k - 1] = np.mean( (X0 - Xhat0) ** 2 )\n",
    "plt.plot(K, mse)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e40bf4ab",
   "metadata": {},
   "source": [
    "For each K from 1 to 30, compute the mean squared error in the SVD approximation and plot as a line graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f752db03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gWsnW08fSs0qy9QOy9DeT6AcEAJinCCAAgAsCCADgggACALgggAAALgggAIALAggA4IIAAgC4IIAAAC4IIACACwIIAOCCAAIAuCCAAAAuCCAAgIusbccwNTUVtN39+Pi4aVzPdgyWekutdbt4yzG3ts+wsLREkGxtDSxjW1tYWNaKdez8/PC/81pqLee1ZGuJYH1fsJyf1p+bdgwAgHmJAAIAuCCAAAAuZh1Ae/bs0fr161VbW6u8vDzt3LlzxuMPP/yw8vLyZtzWrVuXqfkCAOaJWQfQ8PCwVq5cqba2tvM+Z926dTpx4sT07a233jJNEgAw/8z6U3BNTU1qamq64HPi8biSyWTwpAAA89+c/A5o9+7dqqqq0vXXX6/HH39cvb29533u+Pi4BgYGZtwAAPNfxgNo3bp1euONN9Te3q6XXnpJHR0dampqUiqVOufzW1tblUgkpm91dXWZnhIAIAtl/D+iPvDAA9N/vummm7RixQpdffXV2r17t+6+++5vPX/r1q1qaWmZ/npgYIAQAoBLwJx/DHvZsmVavHixDh8+fM7H4/G4ysvLZ9wAAPPfnAfQ8ePH1dvbq5qamrkeCgCQQ2b9T3BDQ0MzrmY6Ozv15ZdfqrKyUpWVlXr++ee1ceNGJZNJHTlyRE8//bSuueYaNTY2ZnTiAIDcNusA+vzzz3XXXXdNf3329zebNm3S9u3b9Y9//EN/+tOf1NfXp9raWq1du1a/+tWvFI/HMzdrAEDOm3UA3XnnnRfcEfcvf/mLaUIAgEsDe8EBAFxkbT+gVCoV1A/I2l/G0vdjcHDQNHZ/f39wraXniPWYTU1NBdeeOXPGNLalF1FJSYlp7NLS0uDaBQvCTz1rzytLf5mQc/K/VVZWBtdaXi/rMbP8B3nLeS3Zzm3rzz05ORlURz8gAEBWI4AAAC4IIACACwIIAOCCAAIAuCCAAAAuCCAAgAsCCADgggACALgggAAALgggAIALAggA4IIAAgC4IIAAAC6yth2DpAs2vjsfS2sASRobGwuutbZj6O3tDa61tDWorq4OrpWkhQsXBtcWFBSYxk6lUsG1ltYbkpSfH/73N0s7BssalWzniKUFhSQVFxcH11pea0s7BUk6depUcK215Yjl9Q5tp3BW6DG/2PduroAAAC4IIACACwIIAOCCAAIAuCCAAAAuCCAAgAsCCADgggACALgggAAALgggAIALAggA4IIAAgC4IIAAAC4IIACAi6xux5CXlzfrmpAWDv/Nsn350NCQaeyTJ08G13Z1dQXXLlq0KLhWsrVUsG7vH4vFgmvT6bRpbEs7hsLCQpdayXbMLK03pLBz+qy+vr7g2hMnTgTXSlJ3d3dwrbVNi+U9yWuN044BAJDVCCAAgAsCCADgggACALgggAAALgggAIALAggA4IIAAgC4IIAAAC4IIACACwIIAOCCAAIAuCCAAAAuCCAAgAsCCADgImv7AeXn5wf1DrH2v7CYmJgw1ff39wfXWvqdWPsBFRUVBddWVVWZxk4kEsG1CxbYlr+lH5BlbOu8Lf2bUqmUaewzZ84E1/b09ATXfv3118G1knT69Ong2rGxMdPYlmNuWaNSeP+mi30f5goIAOCCAAIAuCCAAAAuCCAAgAsCCADgggACALgggAAALgggAIALAggA4IIAAgC4IIAAAC4IIACACwIIAOCCAAIAuMjadgwLFixwaccQuv24ZN+qfnR0NLj2m2++Ca49fvx4cK0kFRcXu9RKUklJSXCtpZWDZJt7YWFhcK11jVvaA/T29prGPnnyZHCtpaWCpZ2CJI2MjATXWt8XLKytO6IoCqqjHQMAIKsRQAAAFwQQAMDFrAKotbVVt9xyi8rKylRVVaUNGzbo4MGDM54zNjam5uZmLVq0SKWlpdq4caOplS4AYH6aVQB1dHSoublZ+/bt08cff6zJyUmtXbtWw8PD08958skn9eGHH+q9995TR0eHurq6dN9992V84gCA3Darj0js2rVrxtc7duxQVVWVDhw4oJ/85Cfq7+/XH/7wB7355pv66U9/Kkl6/fXX9cMf/lD79u3TrbfemrmZAwBymul3QP39/ZKkyspKSdKBAwc0OTmphoaG6ecsX75cS5Ys0d69e8/5PcbHxzUwMDDjBgCY/4IDKJ1Oa8uWLbrtttt04403SpK6u7sVi8VUUVEx47nV1dXq7u4+5/dpbW1VIpGYvtXV1YVOCQCQQ4IDqLm5WV999ZXefvtt0wS2bt2q/v7+6duxY8dM3w8AkBuC/pvs5s2b9dFHH2nPnj264oorpu9PJpOamJhQX1/fjKugnp4eJZPJc36veDyueDweMg0AQA6b1RVQFEXavHmz3n//fX3yySdaunTpjMdXrVqlwsJCtbe3T9938OBBHT16VGvWrMnMjAEA88KsroCam5v15ptv6oMPPlBZWdn073USiYSKi4uVSCT06KOPqqWlRZWVlSovL9cTTzyhNWvW8Ak4AMAMswqg7du3S5LuvPPOGfe//vrrevjhhyVJv/3tb5Wfn6+NGzdqfHxcjY2N+v3vf5+RyQIA5o9ZBdDF7IxaVFSktrY2tbW1BU8KADD/sRccAMBF1vYDisViQb15QvtXnJWfH57JBQUFprEtfV7Gx8eDa629Uk6cOBFca+0HZOmrE4vFTGNb1orltZ6YmAiulaS+vr7gWstrLUldXV3BtZaeV/+9XVgIy/uKZZ1ItnVqfT8MXaf0AwIAZDUCCADgggACALgggAAALgggAIALAggA4IIAAgC4IIAAAC4IIACACwIIAOCCAAIAuCCAAAAuCCAAgAsCCADgImvbMRQWFgZtY27dftzSUiEej7uNnUqlgmstrRwk2/b+lu35JdvrPTo6ahq7vLw8uNbSRmJsbCy4VrK9XtbWHb29vcG1lp/b833B2vbDWm9BOwYAwLxEAAEAXBBAAAAXBBAAwAUBBABwQQABAFwQQAAAFwQQAMAFAQQAcEEAAQBcEEAAABcEEADABQEEAHBBAAEAXBBAAAAXWdsPqKio6JLrB1RUVBRca+kvYzU1NRVcOzg4aBo7ZI2cZe0HVFJSEly7YEH4qRfao+UsS1+dkZER09iW3lOWc9vaU8dybk5MTJjGtpxflvNDCu8zdrF1XAEBAFwQQAAAFwQQAMAFAQQAcEEAAQBcEEAAABcEEADABQEEAHBBAAEAXBBAAAAXBBAAwAUBBABwQQABAFxk3W7YZ3e8Dd3x17obdl5eXnCtdZfi0J1nJduOuZOTk8G1km23X+tOwZbdlS27Qku2teK5G7bnMbOM7bnOLOeI5dyUbO8LllpL/dm673o/zroAOrs9f09Pj/NMAAAWg4ODSiQS5308L7JeMmRYOp1WV1eXysrKzvk3zIGBAdXV1enYsWMqLy93mGHu4ZjNHsds9jhmszdfj1kURRocHFRtbe0FexJl3RVQfn6+rrjiiu98Xnl5+bx6wb4PHLPZ45jNHsds9ubjMbvQlc9ZfAgBAOCCAAIAuMi5AIrH49q2bZvi8bj3VHIGx2z2OGazxzGbvUv9mGXdhxAAAJeGnLsCAgDMDwQQAMAFAQQAcEEAAQBc5FwAtbW16aqrrlJRUZHq6+v12WefeU8paz333HPKy8ubcVu+fLn3tLLKnj17tH79etXW1iovL087d+6c8XgURXr22WdVU1Oj4uJiNTQ06NChQz6TzRLfdcwefvjhb627devW+Uw2C7S2tuqWW25RWVmZqqqqtGHDBh08eHDGc8bGxtTc3KxFixaptLRUGzduvCS2I8upAHrnnXfU0tKibdu26YsvvtDKlSvV2NiokydPek8ta91www06ceLE9O1vf/ub95SyyvDwsFauXKm2trZzPv7yyy/r1Vdf1Wuvvab9+/dr4cKFamxsNG/Kmcu+65hJ0rp162asu7feeut7nGF26ejoUHNzs/bt26ePP/5Yk5OTWrt2rYaHh6ef8+STT+rDDz/Ue++9p46ODnV1dem+++5znPX3JMohq1evjpqbm6e/TqVSUW1tbdTa2uo4q+y1bdu2aOXKld7TyBmSovfff3/663Q6HSWTyejXv/719H19fX1RPB6P3nrrLYcZZp//PWZRFEWbNm2K7rnnHpf55IKTJ09GkqKOjo4oiv6zpgoLC6P33ntv+jn//Oc/I0nR3r17vab5vciZK6CJiQkdOHBADQ0N0/fl5+eroaFBe/fudZxZdjt06JBqa2u1bNkyPfTQQzp69Kj3lHJGZ2enuru7Z6y5RCKh+vp61tx32L17t6qqqnT99dfr8ccfV29vr/eUskZ/f78kqbKyUpJ04MABTU5Ozlhny5cv15IlS+b9OsuZAPrmm2+USqVUXV094/7q6mp1d3c7zSq71dfXa8eOHdq1a5e2b9+uzs5O3XHHHdMtL3BhZ9cVa2521q1bpzfeeEPt7e166aWX1NHRoaamJnNvmvkgnU5ry5Ytuu2223TjjTdK+s86i8ViqqiomPHcS2GdZd1u2Micpqam6T+vWLFC9fX1uvLKK/Xuu+/q0UcfdZwZ5rMHHnhg+s833XSTVqxYoauvvlq7d+/W3Xff7Tgzf83Nzfrqq6/4Xez/lzNXQIsXL1ZBQcG3PhnS09OjZDLpNKvcUlFRoeuuu06HDx/2nkpOOLuuWHM2y5Yt0+LFiy/5dbd582Z99NFH+vTTT2e0nEkmk5qYmFBfX9+M518K6yxnAigWi2nVqlVqb2+fvi+dTqu9vV1r1qxxnFnuGBoa0pEjR1RTU+M9lZywdOlSJZPJGWtuYGBA+/fvZ83NwvHjx9Xb23vJrrsoirR582a9//77+uSTT7R06dIZj69atUqFhYUz1tnBgwd19OjReb/Ocuqf4FpaWrRp0ybdfPPNWr16tV555RUNDw/rkUce8Z5aVnrqqae0fv16XXnllerq6tK2bdtUUFCgBx980HtqWWNoaGjG38w7Ozv15ZdfqrKyUkuWLNGWLVv04osv6tprr9XSpUv1zDPPqLa2Vhs2bPCbtLMLHbPKyko9//zz2rhxo5LJpI4cOaKnn35a11xzjRobGx1n7ae5uVlvvvmmPvjgA5WVlU3/XieRSKi4uFiJREKPPvqoWlpaVFlZqfLycj3xxBNas2aNbr31VufZzzHvj+HN1u9+97toyZIlUSwWi1avXh3t27fPe0pZ6/77749qamqiWCwWXX755dH9998fHT582HtaWeXTTz+NJH3rtmnTpiiK/vNR7GeeeSaqrq6O4vF4dPfdd0cHDx70nbSzCx2zkZGRaO3atdFll10WFRYWRldeeWX02GOPRd3d3d7TdnOuYyUpev3116efMzo6Gv3iF7+IfvCDH0QlJSXRvffeG504ccJv0t8T2jEAAFzkzO+AAADzCwEEAHBBAAEAXBBAAAAXBBAAwAUBBABwQQABAFwQQAAAFwQQAMAFAQQAcEEAAQBcEEAAABf/D5Nbyk0awuJyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imgs = []\n",
    "for j in [1, 2, 3]:\n",
    "    alpha = 2 * np.median(np.abs(W[:,j]))\n",
    "    img = np.reshape(mu+alpha * Vh[j,:],(24,24))\n",
    "    plt.imshow( img.T , cmap=\"gray\")\n",
    "    plt.show()\n",
    "    img = np.reshape(mu-alpha * Vh[j,:],(24,24))\n",
    "    plt.imshow( img.T , cmap=\"gray\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "830ee2cb",
   "metadata": {},
   "source": [
    "Display the first three principal directions of the data by computing μ + αV[j:] and μ - αV[j:], where α is the scale factor"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}